WIAS Preprint No. 45, (1993)

A rigorous renormalization group method for interfaces in random media.


  • Bovier, Anton
  • Külske, Christof

2010 Mathematics Subject Classification

  • 60K40 82B44 82C22 60K35


  • Disordered systems, interfaces, SOS-model, renormalization group, contour models




We prove the existence Gibbs states describing rigid interfaces in a disordered solid-on-solid (SOS) for low temperatures and for weak disorder in dimension D ≥ 4. This extends earlier results for hierarchical models to the more realistic models and proves a long-standing conjecture. The proof is based on the renormalization group method of Bricmont and Kupiainen originally developed for the analysis of low-temperature phases of the random field Ising model. In a broader context, we generalize this method to a class of systems with non-compact single-site state space.

Appeared in

  • Rev. Math. Phys., 6 (1994), pp. 413--496

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